On the prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914187183128576 |
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| author | Voet, Yannis Sande, Espen |
| author_facet | Voet, Yannis Sande, Espen |
| contents | While interpolatory bases such as the Lagrange basis form the cornerstone of classical finite element methods, they have been replaced in the more general finite element setting of isogeometric analysis in favor of other desirable properties. Yet, interpolation is a key property for devising accurate mass lumping strategies that are ubiquitous in explicit dynamic analyses of structures. In this article, we explore the possibility of restoring interpolation for spline bases within isogeometric analysis for the purpose of mass lumping. Although reminiscent of the spectral element method, this technique comes with its lot of surprises and challenges, which are critically assessed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13510 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis Voet, Yannis Sande, Espen Numerical Analysis 65M12, 65M22, 65M60 While interpolatory bases such as the Lagrange basis form the cornerstone of classical finite element methods, they have been replaced in the more general finite element setting of isogeometric analysis in favor of other desirable properties. Yet, interpolation is a key property for devising accurate mass lumping strategies that are ubiquitous in explicit dynamic analyses of structures. In this article, we explore the possibility of restoring interpolation for spline bases within isogeometric analysis for the purpose of mass lumping. Although reminiscent of the spectral element method, this technique comes with its lot of surprises and challenges, which are critically assessed. |
| title | On the prospects of interpolatory spline bases for accurate mass lumping strategies in isogeometric analysis |
| topic | Numerical Analysis 65M12, 65M22, 65M60 |
| url | https://arxiv.org/abs/2510.13510 |